The quaternion is able to describe the physical features of the electromagnetic field and gravitational field. In the quaternion space for the electromagnetic field, the quaternion radius vector combines with the integral of electromagnetic potential to become the compounding radius vector. From the quaternion operator and the compounding radius vector, it is able to deduce the compounding field strength, field source, and wave equation of the electromagnetic field. According to the compounding wave equation, the compounding field strength is one transverse wave, which transmission direction is perpendicular to the electric intensity and magnetic flux density, and is able to impact the movements of other trial charges, and then to form the electromagnetic dense waves. The quaternion space for the gravitational field is independent to that for the electromagnetic field. In the quaternion space for the gravitational field, the quaternion radius vector combines with the integral of gravitational potential to become the compounding radius vector. From the quaternion operator and the compounding radius vector, it is able to deduce the compounding field strength, field source, and wave equation of the gravitational field. According to the compounding wave equation, the compounding field strength is one transverse wave, which transmitted along the orbital tangent direction, and is able to influence the movements of other objects, and then to form the gravitational dense waves.
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